Geometric percolation in chiral nematic liquid crystals of hard particles

In geometric percolation, two particles are connected if their shortest distance is smaller than a cut-off distance known as the connectedness criterion. Clusters are then defined as mutually connected particles. The average number of particles in a cluster increases with particle loading and diverges upon approach of the percolation threshold. The average cluser becomes system-spanning at the percolation threshold, and the physical properties of the dispersion change drastically beyond it.

For fluid dispersions of rod-like particles, the percolation threshold must depend on whether the particles are in the isotropic or in the (chiral) nematic phase, which for long rods appears at very low packing fractions. Theory and simulations have so far focused on percolation in the isotropic phase. It is well-established that for realistic connectedness criteria, percolation occurs near the isotropic-nematic phase transition.

We study percolation in the nematic phase of hard spherocylinders by means of Monte Carlo simulation and connectedness percolation theory. We find that there is a range of values of the connectedness criterion for which percolation occurs in the nematic phase, even when it does not occur in the isotropic phase. This happens if the connectedness criterion drops below a critical value.

We find that clusters of rod-like particles in the nematic phase are highly anisotropic: they are very much longer along the director field than perpendicular to that. Upon approach of the percolation threshold both the length and the width of the clusters diverge with the same critical exponent. We find that for helical rods that support a cholesteric phase the percolation threshold shifts to even larger values, both in the isotropic and in the cholestric phase.